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Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is___________?

Correct answer: C. Rs.5.00

  • A. Rs.3
  • B. Rs.4.50
  • C. Rs.5.00
  • D. Rs.7.50

Explanation

Take the attendance numbers as 2, 5 and 13 units, so total attendance is 20 units. The total collection is 2 x Rs.15 + 5 x Rs.7.50 + 13 x Rs.2.50 = Rs.100, giving an average charge of Rs.100/20 = Rs.5 per person. The likely mistake is choosing Rs.7.50 by taking an ordinary average of the three charges instead of a weighted average based on attendance.

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An average represents the total of a set of values divided by the number of values, and a weighted average gives different importance to different groups. Problems involve missing values, combined averages, replacement of observations, and changes in the average, so the total and count must be tracked separately.

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